No, that is not the case. You can add and remove apps without affecting you other devices on your Google account. When you setup you N7 you selected the option to keep your device backed up, which will only initially install what apps you have currently installed on other devices.

This is the second time I've heard somebody say that apps from another device automatically installed on their Nexus 7, I've not experienced this.I have flashed a multiple custom ROM's on my S2 and had apps automatically install that were backed up but even flashing ROM's on my 7 this had not been the case. And yes I have the backup option checked...

PersonallyI would have been annoyed if apps I use on my S2 were automatically installed on my N7, okay so there are a few that are the same but some are also different.

I was under the impression that it was device to device, so I can understand apps being installed on an upgraded 32GB N7 that were originally installed on another N7 but not apps from another device?

My first Android device was an SE Xperia X10i, flashing custom ROM's on that and apps were automatically installed when backed up but when I got my S2 none of the apps from my X10i were automatically installed on the S2.As I said above, when flashing custom ROM's on my S2, apps that were backed up were automatically installed on the S2, as were Wi-Fi passwords. However, none of those apps or Wi-Fi passwords were installed on my N7, not new out of the box, when it was rooted or the three times I have flashed the factory image.